Log Problem: number t years after 1970 approx. N=4(1.025)^t

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2plus2equals4

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Solve the problem: The number of children N registered in preschool, in millions, t years after 1970 can be approximated by N(t) = 4 (1.025)^t.

a) Find the year in which 10 million children will be registered in preschool.
b) Find the initial # of students registered.

So, I want to make sure that I understand this.

In 1970: 4(1.025)^0 = 4 (million)
In 2007: 4(1.025)^37 = 9.97 (million)
In 2008: 4(1.025)^38 = 10.2 (million)

a) This what I am unsure of: The year will be 2007 or 2008 when 10 million children will be registered in preschool? I'm not sure how far to round. Technically, there are not 10 million yet in 2007. Any suggestions?
b) 4 million were the initial number of students registered. Right?
 
Re: Log Problem

2plus2equals4 said:
Solve the problem: The number of children N registered in preschool, in millions, t years after 1970 can be approximated by N(t) = 4 (1.025)^t.

a) Find the year in which 10 million children will be registered in preschool.
b) Find the initial # of students registered.

So, I want to make sure that I understand this.

In 1970: 4(1.025)^0 = 4 (million)
In 2007: 4(1.025)^37 = 9.97 (million)
In 2008: 4(1.025)^38 = 10.2 (million)

a) This what I am unsure of: The year will be 2007 or 2008 when 10 million children will be registered in preschool? I'm not sure how far to round. Technically, there are not 10 million yet in 2007. Any suggestions?

I would answer 2008 - assuming the enrollment is at the begining of the year. The correct wording of the problem would be - Find the year in which 10 million children will be registered in preschool - for the first time. This is because there will be 10 million (and more) student registered in 2009, 2010, and so on.

b) 4 million were the initial number of students registered. Right? >>>>> Correct
Click to expand...
 
Re: Log Problem

Solve the problem: The number of children N registered in preschool, in millions, t years after 1970 can be approximated by N(t) = 4 (1.025)^t.

a) Find the year in which 10 million children will be registered in preschool.
b) Find the initial # of students registered.

So, I want to make sure that I understand this.

In 1970: 4(1.025)^0 = 4 (million)
In 2007: 4(1.025)^37 = 9.97 (million)
In 2008: 4(1.025)^38 = 10.2 (million)

a) This what I am unsure of: The year will be 2007 or 2008 when 10 million children will be registered in preschool? I'm not sure how far to round. Technically, there are not 10 million yet in 2007. Any suggestions?
b) 4 million were the initial number of students registered. Right?
Click to expand...

Everything you’ve done/stated is fine. Four million is the initial number of students. Regarding when 10 million occurs, consider setting the left side to 10 and solving:

N(t) = 4 (1.025)^t
10 = 4 (1.025)^t
2.5 = 1.025^t
log 2.5 = log 1.025^t
log 2.5 = t(log 1.025)
t = (log 2.5)/(log 1.025)
t = 37.1

This corresponds to February of 2007. I'd probably vote for 2007 though this is somewhat open to interpretation as already pointed out.
 
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